Cosimo de' Medici was born in Florence to Giovanni di Bicci de' Medici and his wife Piccarda Bueri on 10 April 1389. At the time, it was customary to indicate the name of one's father in one's name for the purpose of distinguishing the identities of two like-named individuals; thus Giovanni was the son of Bicci, and Cosimo's name was properly rendered Cosimo di Giovanni de' Medici. He was born along with a twin brother Damiano, who survived only a short time. The twins were named after Saints Cosmas and Damian, whose feast day was then celebrated on 27 September; Cosimo would later celebrate his own birthday on that day, his 'name day', rather than on the actual date of his birth. Cosimo also had a brother Lorenzo, known as 'Lorenzo the Elder', who was some six years his junior and participated in the family's banking enterprise.

In the realm of philosophy, Cosimo, influenced by the lectures of Gemistus Plethon, supported Marsilio Ficino and his attempts at reviving Neo-Platonism. Cosimo commissioned Ficino's Latin translation of the complete works of Plato (the first ever complete translation) and collected a vast library that he shared with intellectuals such as Niccola de' Niccoli and Leonardo Bruni. He also established a Platonic Academy in Florence in 1445. He provided his grandson Lorenzo de' Medici with an education in the studia humanitatis. Cosimo certainly had an influence on Renaissance intellectual life, but it was Lorenzo who would later be deemed to have been the greatest patron.